Pipes Of Variable Cross-section Research Articles

Statistical Problems for the Generalized Burgers Equation: High-Intensity Noise in Waveguide Systems

A one-dimensional equation is presented that generalizes the Burgers equation known in the theory of waves and in turbulence models. It describes the nonlinear evolution of waves in pipes of variable cross section filled with a dissipative medium, as well as in ray tubes, if the approximation of geometric acoustics of an inhomogeneous medium is used. The generalized equation is reduced to the common Burgers equation with a dissipative parameter—the “Reynolds–Goldberg number,” depending on the coordinate. The method for solving statistical problems corresponding to specified characteristics of a noise signal at the input of the system is described. Integral expressions for exact solutions are given for the correlation function and the noise intensity spectrum experiencing nonlinear distortions during propagation in a waveguide. For waves in a dissipative medium, an approximate method of calculating statistical characteristics is given, consisting in finding an auxiliary correlation function and the subsequent nonlinear functional transformation. Solutions have a complicated form, so physical analysis of phenomena requires the numerical methods. For some correlation functions of stationary noise with initial Gaussian statistics and some waveguide systems, it is possible to obtain simple results.

Rarefied gas flow through a pipe of variable square cross section into vacuum

The kinetic S-model is used to study the steady rarefied gas flow through a long pipe of variable cross section joining two tanks with arbitrary differences in pressure and temperature. The kinetic equation is solved numerically by applying a second-order accurate conservative method on an unstructured mesh. The basic quantity to be computed is the gas flow rate through the pipe. The possibility of finding a solution based on the assumption of the plane cross sectional flow is also explored. The resulting solutions are compared with previously known results.

Simulation of flexural waves in drill pipes including the effects of the gravitational field

We design a full-wave modeling method to simulate flexural (bending) waves in pipes of variable cross-section and material properties, subject to the effects of the gravitational field. The study finds application in propagation through drill strings and stability of hydrocarbon wells while drilling. The algorithm is based on a direct (grid) method, where the spatial derivatives are computed with the Fourier pseudospectral method. The modeling is successfully tested against the analytical solution for flexural waves propagating in a uniform pipe. Moreover, we obtain reciprocity relations for the lateral deflection, particle velocity and bending moment due to sources applied in the force-balance and constitutive equations. The relations are then verified by the simulations and at the same time provide a test of the consistency of the numerical algorithm in inhomogeneous media, where there is no closed-form analytical solution.We analyze the effects of the gravitational field and show that for negative axial loads (compressive stresses) there is an instability below a critical wavenumber, while the system is stable for positive (tensile) loads. Such a situation appears below the neutral point of a drill string when the gravitational force is taken into account. A plane-wave analysis yields the phase and group velocities when the load is uniform along the pipe and in the case of a suspended pipe subject to a gravitational force with a neutral point downhole. In the latter case, the signal propagates with attenuation. Propagation along a realistic drill string, simulating the drill bit as a stress-free end, is illustrated. Moreover, propagation subject to an axial gravitational load shows that the signal is slower for a tensile prestress.

TVD schemes for the calculation of flow in pipes of variable cross-section

In this paper, first and second order explicit TVD finite difference schemes have been adapted to the calculation of the unsteady one-dimensional flow in ducts of varying cross-sectional area. The basic idea to bear in mind has been the formulation of the schemes in function of the flux instead of the conserved variables, in order to include the term concerning the cross-section variation correctly. The calculation of eigenvalues of Jacobian matrix has been based on the Roe's linearization technique, and a modification of the first and third eigenvalues has been done in order to force the satisfaction of the entropy condition. Numerical results are presented to demonstrate the performance of the proposed scheme.

Heat exchange between three streams in pipes of variable cross section

A method of calculating the thermal characteristics in the interaction of three streams in pipes of variable cross section in the presence of heat exchange with the ambient medium is discussed.

Generalized similarity of laminar nonisothermic flows of a viscous gas in thin pipes of variable cross section

The method of generalized similarity of the boundary-layer theory is applied to the problem of laminar flow of a viscous gas in thin circular pipe with cross section which varies along the length of the pipe.

Study of the motion of powder-gas mixtures in pipes

A set of differential hydrodynamic equations is derived for motion of a powder-laden flow in a pipe of variable cross section with allowance for gas compressibility and heat transfer between the components. The characteristics of the motion of mixtures in nozzles and under steady conditions of gas-pressure transport are demonstrated;